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Description
- Overview:
- This lesson unit is intended to help teachers assess whether students are able to: identify when two quantities vary in direct proportion to each other; distinguish between direct proportion and other functional relationships; and solve proportionality problems using efficient methods.
- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013
- License:
-
Creative Commons Attribution Non-Commercial No Derivatives
- Media Format:
- Downloadable docs, Text/HTML
Comments
Standards
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Degree of Alignment: 3 Superior (1 user)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Recognize and represent proportional relationships between quantities.
Degree of Alignment: 3 Superior (1 user)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Degree of Alignment: 3 Superior (1 user)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.
Degree of Alignment: 3 Superior (1 user)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Degree of Alignment: Not Rated (0 users)
Cluster: Mathematical practices
Standard: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x –1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x^2 + x + 1), and (x – 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Degree of Alignment: Not Rated (0 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Degree of Alignment: Not Rated (0 users)
Common Core State Standards Math
Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Degree of Alignment: Not Rated (0 users)
Cluster: Mathematical practices
Standard: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Recognize and represent proportional relationships between quantities.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems
Indicator: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x -1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x^2 + x + 1), and (x - 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"ť They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Indicator: Recognize and represent proportional relationships between quantities.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Indicator: Solve multi-step real world and mathematical problems involving ratios and percentages.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Indicator: Compute unit rates, including those involving complex fractions, with like or different units.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Decide whether two quantities in a table or graph are in a proportional relationship.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Represent proportional relationships with equations.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Ratios and Proportional Relationships
Standard:
Indicator: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Degree of Alignment: Not Rated (0 users)
Evaluations
Achieve OER
Average Score (3 Points Possible)| Degree of Alignment | 3 (1 user) |
| Quality of Explanation of the Subject Matter | 3 (1 user) |
| Utility of Materials Designed to Support Teaching | 3 (1 user) |
| Quality of Assessments | N/A |
| Quality of Technological Interactivity | N/A |
| Quality of Instructional and Practice Exercises | N/A |
| Opportunities for Deeper Learning | N/A |
Proportion and Non-proportion Situations
I used this resource in grade 7 , the details was good and enough , lesson plan was good organize and covered lots of activity , the power point was useful and can engage the high level students, it has problem solving from real life and this motivate and make the students attention.
khalid ahmed elmaghny
ibn khaldoun prp school
This is a lesson where students can investigate Proportions. The lesson comes with many resources like a Pre-Assessment, activity templates, and detailed lesson plans. It also has a Powerpoint to match the lesson. It addresses CCSS: 7.RP.1: Analyze proportional relationships and use them to solve real-world and mathematical problems. Although the lesson suggests 2-3 days. It has taken my class more like 3-4 days to do these types of investigations. I would suggest giving the Pre-Assessment ahead of time to your class so you can grade it before starting the activities